The bouncing part was a hypothetical, not in-game situation, with the racket not moving at all, to illustrate the effect of the tension on the shuttle.
For strings to be so loose to not get a bounce at all, the tension would have to be unbelievably low and that doesn’t really happen. If you string a racket at 20 lbs and leave it for 10 years, it will still have a bounce.
To control the bounciness when hitting soft shots, players can ‘cut’ the shuttle, like giving spin in tennis. Instead of having the racket face move straight into the shuttle, it moves into the shuttle, but at the hitting point there is also perpendicular movement of the racket face relative to the shuttle.
As for tension, I’m sure it has been covered in other threads, but let’s do it again anyway.
A trampoline that has a low tension (but isn’t slack) is much easier to force down. It takes less force to force the trampoline surface down. When the trampoline springs back to flat, it gives the same force back. A trampoline with a higher tension needs a greater force to force it all the way down and when it springs back to flat, it give that same greater force back. Therefore, the tighter trampoline can launch an object higher than a looser trampoline.
But here is where a lot of people go wrong. They understand this analogy and conclude that a higher tension will give them more power. Which is true, but only if you can force the tight trampoline down to begin with. And that takes a force they might not be able to generate. To play with a higher tension, you need the technique, timing, acceleration, and power to be able to dent the tight strings upon impact with the shuttle. If you fail to dent the strings enough, you won’t impart much force into the shuttle.
All of this means that while a higher tension gives you the potential for a higher maximum power (if you have the ability to use it), a lower tension makes it easier to generate power (because the trampoline is easier to force down) up to a certain point.
The higher the tension, the higher the greatest possible power, but the harder it is to access it. The lower the tension, the lower the greatest possible power, but the easier it is to access the power within the limited range. (this is also why on soft shots, shuttles bounce more on lower tensions, because it takes less to force the strings down).
So to answer your question, a lower tension can limit power, but not because the there is slack in the strings. Instead it limits power for players who can use a higher tension to generate more power.
For the player’s experience, this means that over the course of a stringjob’s life, as it loses a little tension, it will gradually become easier to play with, but you will also lose that extra ‘oomph’ in full power smashes.